22 SHINKISHI HATAI 



2. When however the lengths of the internodes for given 

 diameters in different sized frogs are compared, the larger frog 

 has for a given diameter longer internodes than the smaller frog. 

 Thus in this case the internode varies according to the relation 

 given by the following general exponential equation 



V = Ae hx 



where the constants A and h are to be determined from the 

 observations, y is the internodal length, x the diameter and e 

 the base of the natural system of logarithms. 



3. The equation just mentioned expresses also the relation in 

 these two characters in the different segments of the leg from the 

 same frog. 



4. Therefore the rate of the increment of the length of the inter- 

 node following the increase in the diameter is proportional to the 

 length of th? mternode itself, or in mathematical terms. 



d y *, 



dx = hV 



This may be considered as the general formula which expresses 

 the relation of the two characters in different segments of the 

 leg of the same frog as well as in corresponding segments from 

 frogs of different sizes. 



II. Analysis of Boycott's Data 



a. Analytical Constants 



For future reference I shall present here the various values of 

 the analytical constants as determined from Boycott's data. 



